Debug and re-enable flaky browser tests related to focusing

[bkrmendy]

Edit from Balazs: the tests already had a custom timeout, which I increased recently, which made the problem go away for a couple of days. I think what happens is that we are making these tests slower and slower, and eventually they tip over the timeout on the CI

The tests in question:

#6336
#6343

[balazsbajorics]

editing the issue to reflect that increasing the timeout have been making the tests more reliable. I think what happens is that something makes these tests slower and slower, and then they become flaky again.